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JEE Main2015MathematicsParabolaActual

Let O be the vertex and Q be any point on the parabola, x 2 = 8 y . If the point P divides the line segment O Q internally in the ratio 1 : 3 , then the locus of P is

Options

  1. Ax 2 = 2 y
  2. Bx 2 = y
  3. Cy 2 = x
  4. Dy 2 = 2 x

Correct answer

A. x 2 = 2 y

Step-by-step solution

General point on x 2 = 8 y is Q 4 t , 2 t 2 Let P h , k divide O Q in ratio 1 : 3 h , k = 1 4 t + 3 0 1 + 3 , 1 2 t 2 + 3 0 1 + 3 h , k = t , 2 t 2 4 h = t  &  k = t 2 2 k = h 2 2 ⇒   x 2 = 2 y is the required locus.

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